This paper proposes a novel transversal filter and an optimal LMS algorithm, and show how these can be realized as an adaptive equalizer. The transversal filter consists of a walsh and block pulse functions. in the LMS algorithm with equalizers, the convergence factor is an improtant design parameter because it governs stability and convergence speed. The conventional adaptation techniques use a fixed time constant convergence factor by the trial and error method. In this paper, an optimal method in the choice of the convergence factor is proposed. The proposed algorithm is obtrained that is tailored for each filter tap and is updated at each iteration. The performance of the proposed algorithm is compared iwth those of the conventional TDL and DFT equalizers by computer simulations.